Solving a Rational Inequality by Cases
Inequalities and absolute value
warmup
Solve
\[
\frac{x-7}{x+3} > 2
\]
algebraprecalculusinequalitiesrational-inequalitycase-analysisalgebraic-manipulationsolve-inequalityreal-numbers
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What you need first
- solving linear inequalities
- understanding that multiplying an inequality by a negative number reverses the sign
- finding the intersection of two inequalities
What this problem tests
Tests the student's awareness that multiplying an inequality by a variable expression requires knowing its sign, and their ability to manage multiple cases.
This is a standard precalculus or introductory calculus problem, testing the foundational skill of manipulating inequalities correctly.
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